A294490 Triangle read by rows: T(n,k) is the number of simple connected graphs on n vertices having independence number k.

1, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 11, 8, 1, 0, 1, 34, 63, 13, 1, 0, 1, 103, 524, 205, 19, 1, 0, 1, 405, 5863, 4308, 513, 26, 1, 0, 1, 1892, 100702, 135563, 21782, 1105, 34, 1, 0, 1, 12166, 2880002, 7161399, 1576634, 84185, 2140, 43, 1, 0, 1, 105065, 138772607, 652024627, 203380116, 12140094, 274156, 3845, 53, 1, 0

Offset: 1

Author

Andrew Howroyd, Oct 31 2017

Keywords

• nonn
• tabl

Comments

Bivariate inverse Euler transform of A263341. This sequence can be derived from A263341 because the independence number of a disconnected graph is the sum of the independence numbers of its components. - Andrew Howroyd, Feb 19 2020

Examples

			Triangle begins:
  1;
  1,   0;
  1,   1,    0;
  1,   4,    1,    0;
  1,  11,    8,    1,   0;
  1,  34,   63,   13,   1,  0;
  1, 103,  524,  205,  19,  1, 0;
  1, 405, 5863, 4308, 513, 26, 1, 0;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..91 (first 13 rows derived from Brendan McKay data in A263341)

Crossrefs

Columns 2..5 are A243781, A243782, A243783, A243784.

Row sums give A001349.

Cf. A263341 (not necessarily connected).

Extensions

Terms a(56) and beyond derived from A263341 added by Andrew Howroyd, Feb 19 2020